The primary objectives of this study are to determine if rigosertib sodium, given orally in the form of soft gel capsules, is safe and is associated with a reduction in the number of blood transfusion units that are needed in patients with myelodysplastic syndrome (MDS) classified as Low or Intermediate-1 (Int-1) (any cytogenetics) or trisomy 8 Intermediate 2 (Int-2) in the International Prognostic Scoring System (IPSS) who are transfusion-dependent. Rigosertib will be taken on days 1 to 21 of a 21-day cycle.